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Full text of "Mathematical And Physical Papers - Iii"

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43. When the motion is so slow that the part of the resistance which depends on the square of the velocity may be neglected, we have, supposing V to be the terminal velocity,  F=7rg(<Tp) a8, where g is the force of gravity, and o-, which is supposed greater than p, the density of the sphere. Substituting in (126) we get
Let us apply this equation to determine the terminal velocity of a globule of water forming part of a cloud. Putting g= 386, pf = (-116)2, an inch being the unit of length, and supposing o-p"1  1 = 1000, in order to allow a little for the rarity of the air at the height of the cloud, we get V= 6372 x lOOOa2. Thus, for a globule the one thousandth of an inch in diameter, we have V = 1*593 inch per second. For a globule the one ten thousandth of an inch in diameter, the terminal velocity would be a hundred times smaller, so as not to amount to the one sixtieth part of an inch per second.
We may form a very good judgment of the magnitude of that part of the resistance which varies as the square of the velocity, and which is the only kind of resistance that could exist if the pressure were equal in all directions, by calculating the numerical value of the resistance according to the common theory, imperfect though it be. It follows from this theory that if h be the height due to the velocity V9 the resistance is to the weight as 3ph to Sera. For V T593 inch per second, the resistance is not quite the one four hundredth part of the weight; and for a sphere only the one ten thousandth of an inch in diameter, moving with the velocity calculated from the formula (127), the ratio of the resistance to the weight would be ten times as small. The terminal velocities of the globules calculated from the common theory would be 32*07 and 10*14 inches per second, instead of only T593 and '01593 inch. It appears then that the apparent suspension of the clouds is mainly due to the internal friction of air.
44. The resistance to the globule has here been determined as if the globule were a solid sphere. In strictness, account ought to be taken of the relative motion of the fluid particles forming the globule itself. Although it may readily be imagined that no